A P45 is only valid if the date of leaving the last job is in the same tax year as the new job. It is used by the new employer to get your year to date taxable pay, tax paid and tax code.
If you have been claiming Job Seekers Allowance since last September then the Job Centre would have asked for parts 2 & 3 from your P45.
As others have said, P46 is what you need to fill in, which is a declaration saying that the new job is your only or main employment.
And congratulations on the new job!